It's not necessarily the pump, there are other things to check first. If the filter is clean, look at the drain hose - sometimes there's a blockage in it or it's bent in a weird way. Also make sure the hose isn't frozen or clogged (sounds silly but it happens). And then check if you hear the pump running when the drain cycle is supposed to start - it makes a little characteristic noise.
After that, you can also check the one-way valve that stops water from flowing back, sometimes it gets stuck. Where I live for example, we had really hard water and the valve got blocked. If the pump is actually running but the water isn't coming out, or if you hear nothing at all, then yeah it's probably the pump. On a 2008 machine it's possible, pumps wear out after 15+ years.
Before you call someone, you could also do a test: empty the water by hand and run just the drain cycle empty, that'll let you hear better if the pump is working. If you're not too comfortable poking around in the machine, it's true that it's better to call, but at least you can tell the repair person what you've already tested.